Variable discretization method for flow simulation on complex geological models

Abstract

A variable discretization method for general multiphase flow simulation in a producing hydrocarbon reservoir. For subsurface regions for which a regular or Voronoi computational mesh is suitable, a finite difference / finite volume method (“FDM”) is used to discretize numerical solution of the differential equations governing fluid flow (101). For subsurface regions with more complex geometries, a finite element method (“FEM”) is used. The invention combines FDM and FEM in a single computational framework (102). Mathematical coupling at interfaces between different discretization regions is accomplished by decomposing individual phase velocity into an averaged component and a correction term. The averaged velocity component may be determined from pressure and averaged capillary pressure and other properties based on the discretization method employed, while the velocity correction term may be computed using a multipoint flux approximation type method, which may be reduced to two-point flux approximation for simple grid and permeability fields.

Description

CROSS-REFERENCE TO RELATED APPLICATION[0001]This application is the National Stage entry under 35 U.S.C. 371 of PCT / US2011 / 047612 that published as WO 2012 / 071090 and was filed on 12 Aug. 2011, which claims the benefit of U.S. Provisional Application No. 61 / 416,449, filed on 23 Nov. 2010, each of which is incorporated by reference, in its entirety, for all purposes.FIELD OF THE INVENTION[0002]This invention relates generally to the field of development of oil or gas fields, and more particularly to reservoir simulation. Specifically, the invention is a method for numerically solving fluid flow equations in complex subsurface geometries.BACKGROUND OF THE INVENTION[0003]Accurate prediction of flow behaviors in reservoirs is essential for effective reservoir management. Reservoir simulation is the use of a physical model of a reservoir on a computer to test how the reservoir will perform as production or stimulation proceeds over time, i.e. over a series of discrete time steps. The res...

AI Technical Summary

Benefits of technology

The invention is a method for simulating how oil and gas move through a reservoir. It involves creating a computer model of the reservoir and solving differential equations to determine how much oil and gas there are in each cell. The method uses a combination of finite element discretization and finite difference or volume discretization methods to cover the entire model. The flow rates of each oil and gas phase are computed consistent with each other across all regions and interfaces between them. The calculated results can be stored or displayed on a computer screen. Overall, the invention provides a way to accurately model the movement of oil and gas in a reservoir to improve oil and gas production.

Problems solved by technology

Unfortunately, finite difference methods such as two-point flux approximation (TPFA) require Voronoi grids, where each cell boundary is perpendicular to the line joining centers of the two neighboring cells; see, for example, Heinrich.

This is a severe limitation because building a Voronoi grid is challenging if not impossible when a reservoir model contains intersecting faults, pinchouts, or other irregular geological features.

Finite element methods, on the other hand, are more complex mathematically, more difficult to implement, and take longer to execute.

Because of the implementation and efficiency issues associated with finite element and other alternatives, finite difference / finite volume methods such as TPFA are used in practice sometimes in situations where they should not, throwing into doubt the validity of simulation results.

While extensive studies exist in literature on mathematical theory of finite difference / finite volume methods for reservoir simulation, papers published on application of finite element methods to modeling general multiphase (gas or liquid) flow are limited.

Images